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Let A and B be two finite dimensional algebras over an algebraically closed field, related to each other by a stable equivalence of Morita type. We prove that A and B have the same number of isomorphism classes of simple modules if and only if their 0-degree Hochschild Homology groups HH0(A) and HH0(B) have the same dimension. The first of these two equivalent conditions is claimed by the Auslander-Reiten...
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